Fractions

A fraction represents a part of a whole. It consists of a numerator and a denominator, separated by a horizontal line. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts that make up a whole.

Types of Fractions

There are several types of fractions, including:

Proper fraction: When the numerator is less than the denominator (e.g., 3/4).
Improper fraction: When the numerator is greater than or equal to the denominator (e.g., 7/4).
Mixed number: A whole number combined with a proper fraction (e.g., 1 3/4).
Equivalent fractions: Fractions that represent the same part of a whole (e.g., 1/2 and 2/4).

Operations with Fractions

Fractions can be added, subtracted, multiplied, and divided. The following are the basic operations with fractions:

Addition and Subtraction

When adding or subtracting fractions with the same denominator, simply add or subtract the numerators and keep the common denominator.

Example:
¹/₄ + ³/₄ = ⁴/₄ = 1

Multiplication

To multiply fractions, multiply the numerators together and the denominators together.

Example:
²/₃ * ³/₄ = ⁶/₁₂ = ¹/₂

Division

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

Example:
²/₃ ÷ ³/₄ = ²/₃ * ⁴/₃ = ⁸/₉

Comparing and Ordering Fractions

To compare fractions, find a common denominator and then compare the numerators. To order fractions, express them with the same denominator and then compare the numerators.

Conversion to Decimals and Percentages

To convert a fraction to a decimal, divide the numerator by the denominator. To convert a fraction to a percentage, first convert it to a decimal and then multiply by 100.

Practice Problems

1. Add the following fractions: ¹/₃ + ²/₅ 2. Multiply the following fractions: ³/₄ * ²/₇ 3. Compare the following fractions: ²/₅ and ³/₈ 4. Convert ⁵/₆ to a decimal and then to a percentage.

Once you have worked through these problems, you should have a good understanding of the basic concepts and operations involving fractions. Feel free to reach out if you need further clarification or additional practice problems.